Maybe for your group. Like I said, I don't think this is nearly as typical or expected as you seem to be suggesting it is (or ought to be).
Yeah, it's more "ought to be", I think. Silly comparison in a way, but my father once told me that if people waited until they were ready to be parents to have kids, no one would have kids. Same thing here....you have to do it to learn it. And others have to be willing to let you learn it, and try and help with that.
I'm not saying that my suggestions would work for everyone....there will always be exceptions. But I just think that the more we treat DMing as this difficult job that only few are suited for, the more likely that will be exactly what it is.
My players are my family. I mainly play, because my kids asked to learn the game. However, even though most of them are teens, they are nowhere near ready to take on the role of the DM. I am currently working on getting them to take better notes (a skill some of them GREATLY need in school as well). I am also working on getting them to review certain parts of the PHB before each session. In time, hopefully some of them will be able to take some of the maintenance chores off of me, but for the foreseeable future, I am the only one who does this. And it is a TON of work, especially since I am just as new to this as the oldest kid at home is.
I would LOVE to have another group nearby in which I could just be a player and learn from that end, but even if my very full schedule would allow that, we live in too small of a community. I have thought about finding an online game, but the schedule thing is an issue.
First off, that's awesome that you learned the game for your kids!
Being a new DM and also having new players....who also happen to be your children....that's gonna be a pretty tricky thing. The note taking is probably a great start because, as you say, it has potential to be helpful in real life.
If they're teens, then I'd likely suggest testing the waters a bit to see what they can do to help. You may be surprised. And if not, then you know for sure they're not ready for certain things.
Something like looking up a rule or spell that's come up. Instead of play halting entirely while you look up the spell, have one of the kids do it, while you move on the next player's turn. After he next player has gone, have the other one read the spell entry so you can all determine how it worked. That kind of thing.
I usually start off each session by asking one of the players to remind me what happened. Usually, everyone jumps in to help summarize everything that happened, and then we get started. I find that's a good way to engage them quickly.
Maybe use index cards for initiative, and have one of them cycle through the cards after each turn and announce who's next.
It's certainly possible that these ideas may not work, but I'd say give it a try. You may find your job getting a bit easier as DM, and maybe the kids get a better grasp of all the things that are going into the game. I know they're young, but my friends and I were pre-teens when we really got going with D&D, and I'm sure plenty of other folks on these boards started at a similar age. We were far from perfect at it, and there were plenty of things that we pretty much made up our own way of doing, but we were having fun and learning.